ON PROJECTIVE L- MODULES

The concepts of free modules, projective modules, injective modules and the likeform an important area in module theory. The notion of free fuzzy modules was introducedby Muganda as an extension of free modules in the fuzzy context. Zahedi and Ameriintroduced the concept of projective and injective L-modules. In this paper we give analternate definition for projective L-modules. We prove that every free L-module is aprojective L-module. Also we prove that if μ∈L(P) is a projective L-module, and if0→η f→ ν g→ μ →0 is a short exact sequence of L-modules then η⊕ μ >ν.Further it is proved that if μ∈L(P) is a projective L-module then μ is a fuzzy direct summandof a free L-module.